In the following dimensionally correct equation `F=(X)/("Linear Density")`, where F is the force. What is the dimensional formula for X?

Options

A. `M^(0)L^(0)T^(0)`
B. `M L T^(-2)`
C. `M^(2)L^(-2)T^(-2)`
D. `M^(2)L^(0)T^(-2)`

Answer

d

Explanation

By using the principle of homogeneity of dimensions,
`|F|=|(X)/("Linear density")|" ... (1)"`
But linear density = mass per unit length
`therefore` [Linear density] `=[(M)/(L)]=[M^(1)L^(-1)]" ... from (1)"`
`therefore [L^(1)M^(1)T^(-2)]=[(X)/(M^(1)L^(-1))]`
`therefore [X]=[M^(2)L^(0)T^(-2)]`